Introduction to Proof-based Discrete Mathematics

This course will introduce you to higher-level mathematical argumentation and proof, an understanding of which is crucial to making the transition from high school to undergraduate math coursework. What we take as given early on in the study of mathematics actually has reasoning behind it, and this course will show you how to begin to uncover and articulate that reasoning for yourself. To do so, we will focus on the seemingly simple question, “How do we count?”  Answering this question will require thinking in terms of sets rather than numbers, so we will begin with naïve (as opposed to axiomatic) set theory and basic set operations, then see how these operations correspond to counting problems including infinite sets. We will also consider topics such as paradoxes of infinity, countability and uncountability, and advanced theories about counting. On a daily basis, students will attend lectures, work in small groups, and present their mathematical arguments and findings in a mutually supportive, inclusive, and welcoming space.

See sample syllabus here.